On the existence of translating solutions of mean curvature flow in slab regions

Theodora Bourni, Mat Langford, Giuseppe Tinaglia

We prove, in all dimensions $n\ge 2$, that there exists a convex translator lying in a slab of width $\pi \sec \theta$ in ${\mathbb{R}}^{n+1}$ (and in no smaller slab) if and only if $θ\in[0…